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1.
We investigate the steady compressible Navier–Stokes system of equations in the isentropic regime in a domain with several
conical outlets and with prescribed pressure drops. Existence of weak solutions is proved and estimate of these solutions
with respect to the pressure drops is derived under the hypothesis γ > 3 where γ is the adiabatic constant. 相似文献
2.
A. A. Chesnokov 《Journal of Applied Mechanics and Technical Physics》2006,47(6):800-811
The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal
fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant
vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations
resulting from the nonlinear interaction of the specified shear flows is established.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006. 相似文献
3.
The classical exponentially decaying wall jet considered independently by Tetervin (NACA TN 1644 40 pp, 1948), Akatnov (Leningrad Politek Inst Trudy 5:24–31, 1953) and Glauert (J Fluid Mech 1:625–643, 1956) as well as its algebraically decaying counterpart (which will be referred to hereafter as “algebraic Glauert Jet”, or AG-jet for short) belong to the same similarity class of solutions of the boundary layer equations. We investigate in this paper the thermal characteristics of a nonpreheated AG-jet over a permeable wall for prescribed constant wall temperature and prescribed constant heat flux. Their scaling behavior for small and large values of the Prandtl number is discussed in detail and compared to that of the classical Tetervin–Akatnov–Glauert wall jet. 相似文献
4.
5.
A class of steady similarity solutions of the equations for viscous vortex cores which correspond to external inviscid similarity
solutions with a power-law variation of the circumferential velocityv-r
−m near the rotation axis is considered. It is found that if the Bernoulli function in external flow is constant, then these
solutions will exist only on a certain range of the indexm of the exponential. For eachm on this range there are two solutions.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 38–43, January–February,
1998.
The work was financially supported by the Russian Foundation for Fundamental Research (project No. 95-01-00483). 相似文献
6.
The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel
to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear
partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved
numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity
profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting
parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is
found that the problem admits dual solutions. 相似文献
7.
We prove the existence of rotating star solutions which are steady-state solutions of the compressible isentropic Euler–Poisson
(Euler–Poisson) equations in three spatial dimensions with prescribed angular momentum and total mass. This problem can be
formulated as a variational problem of finding a minimizer of an energy functional in a broader class of functions having
less symmetry than those functions considered in the classical Auchmuty–Beals paper. We prove the non-linear dynamical stability
of these solutions with perturbations having the same total mass and symmetry as the rotating star solution. We also prove
finite time stability of solutions where the perturbations are entropy-weak solutions of the Euler–Poisson equations. Finally, we give a uniform (in
time) a priori estimate for entropy-weak solutions of the Euler–Poisson equations. 相似文献
8.
Boyan Sirakov 《Archive for Rational Mechanics and Analysis》2010,195(2):579-607
We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of
the Hamilton–Jacobi–Bellman–Isaacs type with unbounded ingredients and quadratic growth in the gradient without hypotheses
of convexity or properness. Some of our results are new even for equations in divergence form. 相似文献
9.
Sébastien Novo 《Journal of Mathematical Fluid Mechanics》2005,7(4):485-514
In the paper [7], author gives a definition of weak solution to the nonsteady Navier–Stokes system of equations which describes
compressible and isentropic flows in some bounded region Ω with influx of fluid through a part of the boundary ∂Ω. Here, we
present a way for proving existence of such solutions in the same situation as in [7] under the sole hypothesis γ > 3/2 for
the adiabatic constant. 相似文献
10.
The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep
problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions
of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found
by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value
problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form
of operators in the mathematical problem formulation 相似文献
11.
V. V. Pukhnachev 《Journal of Applied Mechanics and Technical Physics》2009,50(2):181-187
The unsteady plane-parallel motion of a incompressible viscoelastic Maxwell medium with constant relaxation time is considered.
The equations of motion of the medium and the rheological relation admit an extended Galilean group. The class of solutions
of this system which are partially invariant with respect to the subgroup of the indicated group generated by translation
and Galilean translation along one of the coordinate axes is studied. The system does not have invariant solutions, and the
set of partially invariant solutions is very narrow. A method for extending the set of exact solutions is proposed which allows
finding solutions with a nontrivial dependence of the stress tensor elements on spatial coordinates. Among the solutions obtained
by this method, the solutions describing the deformation of a viscoelastic strip with free boundaries is of special interest
from a point of view of physics.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 2, pp. 16–23, March–April, 2009. 相似文献
12.
Homogeneous solutions of the elastic equilibrium equations for orthotropic plates are obtained. The normal displacement and
tangential stresses on the flat edges of the plates are zero. Methods to integrate the governing equations are proposed. An
explicit analytic solution for the stress state of a layer with circular or elliptic cavities under a load constant throughout
the thickness is obtained
Translated from Prikladnaya Mekhanika, Vol. 44, No. 8, pp. 114–125, August 2008. 相似文献
13.
A. Yu. Luchka 《Nonlinear Oscillations》2008,11(1):55-69
Methods developed for the solution of general equations with restrictions are applied to the construction of periodic solutions
of systems of differential equations.
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Translated from Neliniini Kolyvannya, Vol. 11, No. 1, pp. 55–70, January–March, 2007. 相似文献
14.
15.
B. N. Elemesova 《Journal of Applied Mechanics and Technical Physics》1999,40(1):28-35
The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence
theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows
with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found
for a polytropic equation of state in a class of isentropic flows.
Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from
Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999. 相似文献
16.
Yu. Yu. Bagderina A. P. Chupakhin 《Journal of Applied Mechanics and Technical Physics》2005,46(6):791-799
All invariant and partially invariant solutions of the Green-Naghdi equations are obtained that describe the second approximation
of shallow water theory. It is proved that all nontrivial invariant solutions belong to one of the following types: Galilean-invariant,
stationary, and self-similar solutions. The Galilean-invariant solutions are described by the solutions of the second Painleve
equation, the stationary solutions by elliptic functions, and the self-similar solutions by the solutions of the system of
ordinary differential equations of the fourth order. It is shown that all partially invariant solutions reduce to invariant
solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 26–35, November–December, 2005. 相似文献
17.
M. A. Abdou 《Nonlinear dynamics》2008,52(1-2):1-9
In this paper, the Exp-function method with the aid of the symbolic computational system Maple is used to obtain the generalized
solitonary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, (2+1)-dimensional
Konopelchenko–Dubrovsky equations, the (3+1)-dimensional Jimbo–Miwa equation, the Kadomtsev–Petviashvili (KP) equation, and
the (2+1)-dimensional sine-Gordon equation. It is shown that the Exp-function method, with the help of symbolic computation,
provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics. 相似文献
18.
We investigate the asymptotic behavior of solutions of linear differential equations with almost constant coefficients and
pulse action at fixed times as t tends to infinity. We establish conditions for the times of pulse action under which there exist values of pulse action for
which the solution of the considered Cauchy problem with initial conditions that coincide with the initial conditions for
a certain (arbitrary but fixed) solution of the original equation without pulse action is bounded, unbounded, or tending to
infinity.
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Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 444–455, October–December, 2005. 相似文献
19.
Solutions of contact mixed boundary-value problems for a plate and for a cylindrical shell are given. These solutions are
obtained with the use of equations for shells constructed by expanding solutions of elasticity theory equations with respect
to the Legendre polynomials. Results of numerical simulations of the stress state in the vicinity of points with changing
conditions on the frontal faces of the shell are presented. The results obtained are compared with analytical solutions of
elasticity theory problems and with solutions obtained on the basis of the classical equations of the shell theory.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 169–176, September–October, 2008. 相似文献
20.
Michael Struwe 《Journal of Mathematical Fluid Mechanics》2007,9(2):235-242
We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result
of Zhou [28]. 相似文献